Before reliable near infrared spectroscopic analysis - the critical sampling proviso. Part 1: Generalised theory of sampling

Kim H. Esbensen, Nawaf Abu-Khalaf

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


Non-representative sampling of materials, lots and processes intended for near infrared (NIR) analysis is often contributing hidden additions to the full Measurement Uncertainty (MUtotal = TSE + TAENIR). The Total Sampling Error (TSE) can dominate over the Total Analytical Error (TAENIR) by factors ranging from 5 to 10 to even 25 times, depending on material heterogeneity and the specific sampling procedures employed to produce the minuscule aliquot, which is the only material analysed. This review (Parts 1 and 2), extensively referenced with easily available complementing literature, presents a brief of all sampling uncertainty elements in the “lot-to-aliquot” pathway, which must be identified and correctly managed (eliminated or maximally reduced) in order to achieve, and to be able to document, fully minimised MUtotal. The more irregular and pervasive the heterogeneity, the higher the number of increments needed to reach ‘fit-for-purpose representativity’. A particular focus is necessary regarding the sampling bias, which is fundamentally different from the well-known analytical bias. Whereas the latter can easily be subjected to bias correction, the sampling bias is non-correctable by any posteori means, notably not by chemometrics, nor statistics. Instead, all sampling operations must be designed to exclude the so-called Incorrect Sampling Errors (ISE), which are the hidden bias-generating agents. The key element in this endeavour is representative sampling and sub-sampling before analysis, as laid out by the Theory of Sampling (TOS), which is presented here in a novel compact fashion along with a complement of selected examples and demonstrations. TOS includes a safeguard facility, termed the Replication Experiment (RE), which enables estimation of the total sampling-plus-analysis uncertainty level (MUtotal) associated with NIR analysis (the RE is, for practical and logistical reasons, found in Part 2). Neglecting the TSE effects from the before-analysis domain is lack of due diligence.

Original languageEnglish
Pages (from-to)291-310
Number of pages20
JournalJournal of Near Infrared Spectroscopy
Issue number6
Publication statusPublished - Dec 2022


  • analysis
  • before analysis
  • MU
  • representative sampling
  • sampling bias
  • Theory of Sampling
  • total Measurement Uncertainty

Programme Area

  • Programme Area 3: Energy Resources


Dive into the research topics of 'Before reliable near infrared spectroscopic analysis - the critical sampling proviso. Part 1: Generalised theory of sampling'. Together they form a unique fingerprint.

Cite this